Exact solution of a triaxial gyrostat with one rotor

  • Antonio Elipe
  • Víctor Lanchares
Original Article


The problem of the attitude dynamics of a triaxial gyrostat under no external torques and one constant internal rotor, is a three degrees-of-freedom system, although thanks to the existence of integrals of motion it can be reduced to only one degree-of-freedom problem. We introduce coordinates to represent the orbits of constant angular momentum as a flow on a sphere. This representation shows that the problem is equivalent to a quadratic Hamiltonian depending on two parameters. We find the exact solution of the orbits in terms of elliptic functions. By making use of properties of elliptic functions we find the solution at each region of the parametric partition from the solution of one region. We also prove that heteroclinic orbits are planar curves.


Attitude motion Gyrostat Elliptic functions 


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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Grupo de Mecánica Espacial and IUMAUniversidad de ZaragozaZaragozaSpain
  2. 2.Department of Mathematics and ComputationUniversidad de la RiojaLogroñoSpain

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